Finite Group Databasebeta

← Prev (#72192549) Next (#72192551) →

C₂²×C₉×C₁₆×C₂₅ #72192550

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 92160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₉×C₁₆×C₂₅
multiplicative	(ℤ/22857)ˣ, (ℤ/30476)ˣ, (ℤ/43308)ˣ, (ℤ/45714)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅×C₈	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₃×C₅×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

441 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₉×C₂₅×C₃₂, C₂×C₄×C₉×C₁₆×C₂₅, C₂³×C₉×C₁₆×C₂₅
maximal normal subgroup of	C₂²×C₉×C₂₅×C₃₂, C₂×C₄×C₉×C₁₆×C₂₅, C₂³×C₉×C₁₆×C₂₅
maximal quotient of	C₂²×C₉×C₂₅×C₃₂, C₂×C₄×C₉×C₁₆×C₂₅, C₂³×C₉×C₁₆×C₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.